Finite amplitude acceleration waves in incompressible BKZ viscoelastic fluids— The propagation condition

A general propagation condition is derived which permits the calculation of the speed of propagation of a second-order acceleration wave passing through a particular non-linear incompressible viscoelastic fluid. The viscoelastic fluid is taken to obey the Bernstein, Kearsley and Zapas single integral constitutive model. The analysis is valid for arbitrary finite amplitude waves propagating through a medium undergoing an arbitrary large deformation. Three examples, rest history, steady simple shearing flow and steady simple extensional flow, are given to demonstrate the utility of the propagation condition.